Stable GeV Ion-Beam Acceleration from Thin Foils by Circularly Polarized Laser Pulses

A stable relativistic ion acceleration regime for thin foils irradiated by circularly polarized laser pulses is suggested. In this regime, the “light-sail” stage of radiation pressure acceleration for ions is smoothly connected with the initial relativistic “hole-boring” stage, and a defined relationship between laser intensity $I_0$, foil density $n_0$, and thickness $l_0$ should be satisfied. For foils with a wide range of $n_0$, the required $I_0$ and $l_0$ for the regime are theoretically estimated and verified with the particle-in-cell code ILLUMINATION. It is shown for the first time by 2D simulations that high-density monoenergetic ion beams with energy above $\mathrm{GeV}/\mathrm{u}$ and divergence of 10° are produced by circularly polarized lasers at intensities of ${10}^{22}\mathrm{W}/{\mathrm{cm}}^2$, which are within reach of current laser systems.

Figure 1

Electron density $n_e/n_c$ and ion density $n_i/n_c$ in the ($z$, $x$) plane at (a) $t=16$, (b) 29, (c) 64, and (d) 107 fs for a foil of $n_0=100n_c$ and $l_0=0.35\mu \mathrm{m}$ irradiated by a CP laser pulse at $I_0=6.3\times {10}^{22}\mathrm{W}/{\mathrm{cm}}^2$. (e)–(h) are the corresponding ion phase space plots ($z$, $v_z$).

Figure 2

Ion density $n_i/n_c$ (a) and phase space ($z$, $v_z$) (d) at $t=107\mathrm{fs}$ for the foil of $n_0=30n_c$, $l_0=1.0\mu \mathrm{m}$ by CP laser at $I_0=1.89\times {10}^{22}\mathrm{W}/{\mathrm{cm}}^2$. (b) and (e) show an unstable ion acceleration case with the same $I_0$ and $l_0$ but $n_0=100n_c$; (c) and (f) show another unstable case with the same $n_0$ and $l_0$ but lower $I_0=1.89\times {10}^{21}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

(a) The peak velocities $v_z$ of ion beams varying with time $t$ the cases, respectively, of Figs. 2a [dark gray (blue)], 2b [light gray (green)], and 2c (black); (b) the corresponding peak value of longitudinal electric fields $E_z$ on ion beams. Points “A,” “B,” and “C” correspond to the transition point from “hole-boring” to “light-sail” stages; “B” and “C” clearly show the discontinuous acceleration profile at the transition of the two stages for the unstable cases.

Figure 4

The energy spectra of ions in the region of $z>10\mu \mathrm{m}$ and $|x|<10\mu \mathrm{m}$ at $t=107\mathrm{fs}$ for the cases, respectively, of Figs. 1 [gray (red)] and 2a [dark gray (blue)], 2b [light gray (green)], and 2c (black).